A new approach to velocity averaging lemmas in Besov spaces

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We develop a new approach to velocity averaging lemmas based on the dispersive properties of the kinetic transport operator. This method yields unprecedented sharp results in critical Besov spaces, which display, in some cases, a gain of one full derivative. Moreover, the study of dispersion allows to treat the case of LxrLvp integrability with r ≤ p. We also establish results on the control of concentrations in the degenerate Lx,v1 case, which is fundamental in the study of hydrodynamic limits of the Boltzmann equation.

Original languageEnglish (US)
Pages (from-to)495-551
Number of pages57
JournalJournal des Mathematiques Pures et Appliquees
Issue number4
StatePublished - Apr 2014


  • Besov spaces
  • Dispersion
  • Kinetic transport equation
  • Velocity averaging

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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